Frequency offset estimation is used to lock a local oscillator frequency of a receiver to an incoming carrier frequency through an automatic frequency control (AFC) loop. If the frequency offset estimate is unbiased and has relatively small variance, the residual frequency error will be small and has negligible impact on the error rate performance of the receiver.
The frequency offset estimation can be based, for example, on known pilot symbols (pilot-based) or detected symbols (decision-directed). For GSM (Global System for Mobile Communications) systems, the pilot symbols correspond to the 26 training symbols transmitted in the middle of every burst comprising 156 symbols. With the pilot-based scheme, the training sequence length may be too short to obtain sufficient noise averaging. The decision-directed scheme utilizes all 142 symbols (excluding 8 guard symbols and 6 tail symbols which do not belong to the payload of a burst), assuming that the symbol decisions have relatively low error rate, e.g. <2%.
VAMOS was introduced in Release 9 of the GSM standard and stands for Voice over Adaptive Multi-user on One Slot. VAMOS doubles the existing GSM network capacity by transmitting two GMSK signals in the same time and frequency. On the downlink, a base station superimposes two GMSK signals by rotating the second signal by 90 degrees relative to the first one. Without loss of generality, it is assumed that the first signal is generated from the transmitted symbol sequence x(n) intended for the user under consideration, and the second signal is generated from the transmitted symbol sequence y(n) intended for the second, interfering user. The major goal of the receiver is to detect x(n) with the minimum error rate by suppressing the interference from the second signal, which can be viewed as an internal interferer, as well as interference from external sources, for example interference from the neighboring cells using the same frequency band as the VAMOS signal. The superimposed signal is a complex-valued Alpha-quadrature phase shift keying (AQPSK) signal carrying symbols x(n)+jαy(n) where α is a parameter used to dynamically adjust the relative power levels of the two signals. In the GSM standard, this power ratio is called Sub-Channel Power Imbalance Ratio (SCPIR) where SCPIR=20 log(1/α). If SCPIR is positive, more power is allocated to the first user, and if SCPIR is negative, more power is allocated to the second user. The standard specifies two receiver performance levels, VAMOS I and VAMOS II. The SCPIR value ranges from −4 to +4 dB for VAMOS-I and from −10 to +10 dB for VAMOS-II. The base station applies any SCPIR value within the range to a transmitted burst without signaling. Eight new training sequences TS-9 through TS-16 are introduced and used together with the eight legacy training sequences TS-1 through TS-8. If the first user is assigned TS-1, then the second user will be assigned TS-9, and so on. This way, each user knows both training sequences in a received AQPSK burst.